+ All Categories
Home > Documents > Qqq Collar Study

Qqq Collar Study

Date post: 02-Jun-2018
Category:
Upload: scribd-download
View: 219 times
Download: 0 times
Share this document with a friend

of 46

Transcript
  • 8/10/2019 Qqq Collar Study

    1/46

    Loosening Your Collar: Alternative Implementations of QQQ Collars

    Edward Szado *

    Thomas Schneeweis **

    Original Version: August 2009Current Update: September 2009

    *Doctoral Candidate, Isenberg School of Management, Research Analyst at CISDM, Universityof Massachusetts, Amherst, MA 01003. CISDM gratefully acknowledges research support

    provided by the Options Industry Council. Research results, however, represent those of theauthor and do not necessarily represent the views of the OIC. Please address correspondence toEdward Szado, CISDM, University of Massachusetts, Amherst, MA 01003, 413-577-3166, oremail: [email protected].

    **Michael and Cheryl Philipp Professor of Finance, Director of CISDM, Isenberg School ofManagement, University of Massachusetts, Amherst.

    Abstract

    The credit crisis and the associated decline in equity markets has rekindled new interest in optionbased equity collars and in protective strategies in general. In this paper we consider theperformance of passive and active implementations of the collar strategy on the QQQ ETF aswell as on a sample small cap equity mutual fund. As expected, the results of the analysis showthat a passive collar is most effective (relative to a long underlying position) in declining marketsand less effective in rising markets. This study also considers a more active implementation ofthe collar strategy. Rather than simply applying a set of fixed rules as for the passive collar, inthe active collar adjusted strategy, we apply a set of rules which adapt the collar to varyingeconomic and market conditions. This approach is similar to applying a set of tactical assetallocation rules to a set of investments. There are of course an unlimited number of conditioningfactors that can be used to determine the strategy implementation. In this paper, for purposes ofpresentation, we combine three conditioning factors that have been suggested in academicliterature (momentum, volatility, and a compound macroeconomic factor (unemployment andbusiness cycle)) to generate a dynamic collar adjusted trading strategy. For the period ofanalysis, the active collar adjustment strategy tends to outperform the passive collar. Judgmentsas to the particular benefits of the passive and active collar strategies are, of course, dependent onthe risk tolerance of the individual investor.

  • 8/10/2019 Qqq Collar Study

    2/46

    2

    Introduction

    The credit crisis and the associated decline in equity markets has rekindled new interest

    in option based equity collars and in protective strategies in general. In 2008 the QQQ

    experienced a drawdown of about 50% from peak to trough. Many other asset classes which are

    generally considered effective equity diversifiers also faced significant losses. This type of

    contagion across asset classes suggests that in times of major systematic stress, direct hedges

    through protective option strategies may provide equity portfolios with greater downside risk

    protection than standard multi-asset diversification programs. There are a variety of option

    strategies which can provide capital protection for equity based portfolios. The focus of this

    paper is one of the more straightforward options based strategiesthe collar. A collar is an

    option basedinvestment strategy that effectively limits (or collars) the returns on aninvestment

    in an underlyingasset to fall within a chosen range. An investor who holds a long position in an

    underlying asset can convert that position into a collar (collar his position) by purchasing a put

    option on the underlying asset and simultaneously selling (writing) a call option on the

    underlying asset. Thestrike price on the call defines the upper bound of the collar and is set

    above the strike price for the put (which defines the lower bound of the collar). In a standard

    collar, the call and put have the same expiration dates. The value of a portfolio constructed in

    this manner will essentially be restricted to fluctuate within the bounds set by the strike prices of

    the options (adjusted for the net cost of the option positions).1

    1Collars can be visualized as a combination of covered call and protective put strategies. The collarstrategy essentially adds a long protective put to a covered call strategy. This provides the significantdownside protection which the covered call strategy lacks. The purchase of the long put is financed by thesale of the call. In essence, the collar trades upside participation for downside protection. A tight collarprovides less upside participation and more downside protection than a loose collar. At one extreme, the

    http://en.wikipedia.org/wiki/Investment_strategyhttp://en.wikipedia.org/wiki/Investmenthttp://en.wikipedia.org/wiki/Assethttp://en.wikipedia.org/wiki/Strike_pricehttp://en.wikipedia.org/wiki/Strike_pricehttp://en.wikipedia.org/wiki/Assethttp://en.wikipedia.org/wiki/Investmenthttp://en.wikipedia.org/wiki/Investment_strategy
  • 8/10/2019 Qqq Collar Study

    3/46

    3

    In this paper, we extend previous research on collar strategies (Schneeweis and Spurgin

    [2001] and Szado and Kazemi [2009]) by considering the performance and risk characteristics of

    active as well as passive collars. In addition, we provide an example of the effectiveness of

    applying a collar strategy to a sample equity mutual fund on which options are not available. It is

    worth noting that this study does not address whether these strategies generate alpha based on

    any specific definition of investor risk aversion. The significance of the results may be

    interpreted differently by any individual based on their particular risk aversion.

    In this study the performance of passively implemented collars on the Powershares QQQ

    ETF (ticker: QQQQ) is analyzed. The collars are passive in the sense that they follow a rigid set

    of rules which do not vary with market conditions. The passive implementations do vary in their

    choice of the initial moneyness and time to expiration of the calls and puts. This study also

    considers a more active implementation of the collar strategy. Rather than simply applying a set

    of fixed rules as for the passive collar, for the active collar adjustment strategy, we apply a set of

    rules which adapt the collar to varying economic and market conditions. This approach is similar

    to applying a set of tactical asset allocation rules to a set of investments. There are of course an

    unlimited number of conditioning factors that can be used to determine the strategy

    implementation. In this paper, for purposes of presentation, we combine three conditioning

    factors that have been suggested in academic literature (momentum, volatility, and a compound

    macroeconomic factor (unemployment and business cycle)) to generate a dynamic collar

    adjusted trading strategy.2Finally, the study considers the implementation of an active and

    tightest collar (ATM puts and calls) effectively immunizes the portfolio from market movements. At theother extreme (very far OTM puts and calls), the collar is essentially equivalent to a long index position.2While these collar implementations are active in the sense that the rules are dependent on managerdecisions, they are implemented systematically with no additional manager discretion.

  • 8/10/2019 Qqq Collar Study

    4/46

    4

    passive collar strategy using QQQ options applied to a non-QQQ equity portfolio represented by

    a small cap equity mutual fund. This provides an additional analysis of the use of the collar

    strategy for a wider range of market participants.

    In the following sections we summarize the methodology and data used in this analysis. It

    is important to note that all empirical research may be data and time period dependent. This

    analysis covers the period from the introduction of options on the QQQ (March 19, 1999)

    through May 31, 2009. This period is broken into various sub-periods to offer a better picture of

    the benefits and risk of the implemented collar strategies in various market environments. In the

    methodology section we describe both the passive and active collar implementations. In the

    active collar section we describe how we combine the momentum, volatility and macroeconomic

    signals to generate a dynamic collar adjustment trading strategy process3. In this process, the

    initial moneyness of the puts and calls is determined based on the momentum and

    macroeconomic signals and the ratio of written calls is determined by the volatility signal. The

    marginal effect of the momentum signal is to widen or tighten the collar by increasing or

    decreasing the amount OTM, respectively. The marginal effect of the macroeconomic signal is to

    shift the collar up by increasing the amount OTM of the calls and decreasing the amount OTM of

    the puts, or shift the collar down by moving the strikes in the opposite direction. The marginal

    effect of the volatility signal is to increase or decrease the number of calls written per QQQ and

    put purchased.

    Results show that the passive and active collar strategies underperformed the QQQ in the

    strong market climb of October 2002 to September 2007. However, in the period around the tech

    3While we combine the three signals to generate the strategy, any one of the signals could be used on itsown to generate an active strategy.

  • 8/10/2019 Qqq Collar Study

    5/46

    5

    bubble and in the credit crisis the passive and active collar strategies provided capital protection

    and, in the case of the tech bubble, generated significant returns at relatively low volatility. In

    addition, we provided evidence of the effectiveness of wrapping a passive or active collar

    strategy around a portfolio for which no options are available (in this case, represented by a

    small cap mutual fund). Results for the mutual fund collars are similar to those reported for the

    collar strategies on the QQQ. Finally, results show that active collar strategies on the QQQ and

    on a small cap mutual fund which use a set of three simple trading rules to create a dynamic

    collar adjustment process could provide added benefits over similar passive collars.

    Data and Methodology

    Data

    The option price data is provided by Optionmetrics and covers the period from the first

    expiration after the introduction of QQQ options on March 19, 1999 to May 31, 2009. The QQQ,

    NDX, Treasury bill and VIX data is provided by Datastream4, while mutual fund data is

    provided by Morningstar. Business cycle announcement data are provided by the National

    Bureau of Economic Research.

    Methodology

    In order to assess the performance of active and passive collar strategies, we construct

    indices which represent the return streams generated by such strategies. The passive strategies

    follow a fixed set of option selection rules defining the initial moneyness and time to expiration

    4NDX, VIX and Initial Unemployment Claims data is collected from March 1998 to ensure sufficient lagtime for signal generation.

  • 8/10/2019 Qqq Collar Study

    6/46

    6

    of the calls and puts, regardless of market conditions. In contrast, the active5collar strategies

    base their option selection rules on a combination of three simple market/economic based signals

    (momentum, volatility, and a macroeconomic factor) and thus adjust to various market

    conditions.

    Passive Collar Strategy: We generate a daily time series of returns for each of the passive

    strategies beginning on March 19, 19996. At the close on this day a 1-month call is written and a

    1, 3 or 6-month put is purchased. Depending on the particular passive implementation, the initial

    moneyness of the calls and puts are set at either 5%, 4%, 3%, 2%, 1% OTM or ATM. At the

    close on the Friday prior to the following expiration, we take one of two actions: If 1-month puts

    are used, the puts and calls are settled at intrinsic value and we roll into new 1-month puts and

    calls with the specified moneyness. If a 3- or 6-month put is used, the calls are settled at intrinsic

    value and new 1-month calls with the specified moneyness are rolled into, while the longer term

    put is held for another month. When the new 1-month calls are written, the net proceeds from the

    sale of the calls and the expiration of the previous calls are fully invested in the strategy and the

    position is rebalanced to ensure a 1:1:1 ratio of the underlying, puts and calls. Once the 3- or 6-

    month put expires, it is settled at intrinsic value and we once again roll into new puts and calls

    with the specified moneyness and time to expiration. In order to include the impact of

    transaction costs, the puts are purchased at the ask price and the calls are written at the bid price

    when each new put or call position is established. Each trading day in between roll dates, the

    options are priced at the mid-point between the bid and ask prices. In this manner, daily returns

    5It should be noted that while we use the term active to represent these strategies, they are not trulyactively managed. They still follow an established set of selection rules, but the rules include a dynamicelement conditioned on economic variables.6This is the Friday prior to the first expiration Saturday following the introduction of QQQ options.

  • 8/10/2019 Qqq Collar Study

    7/46

    7

    are calculated for each passive strategy implementation. The following example illustrates this

    process:

    Passive 2% OTM 1-Month Call 6-Month Put ImplementationDate Exdate Quantity Wealth

    Roll In 3 /19 /1999 Purchase QQQ 1.000 @ 102.44$ 108.69$ (Initial)

    Purchase a 6-month 2% OTM put ex pi ri ng on: 9/17/1999 (Strike pri ce = 100) 1.000 @ 9.50$ (at ask)

    Sell a 1-month 2% OTM call expiring on: 4/16/1999 (Strike price = 104) 1.000 @ (3.25)$ (at bid)

    Roll Out 4 /16 /1999 QQQ value 1.000 @ 103.94$ 112.37$

    Ke ep the put (now 5- month 4% OTM) ex pi ri ng on: 9/17/1999 ( Stri ke pri ce = 100) 1. 000 @ 8.44$ (mid of bid/ask)

    Payout value of previous call at expiration: 4/16/1999 (Strike price = 104) 1.000 @ -$ (intrinsic value)

    Roll In 4 /16 /1999 Purchase QQQ 1.037 @ 103.94$ 112.37$

    Ke ep the put (now 5- month 4% OTM) ex pi ri ng on: 9/17/1999 ( Stri ke pri ce = 100) 1. 037 @ 8.44$ (mid of bid/ask)

    Sell a 1-month 2% OTM call expiring on: 5/22/1999 (Strike price = 106) 1.037 @ (4.00)$ (at bid)

    Repeat until put expires

    Roll Out 9 /17 /1999 QQQ value 1.045 @ 126.63$ 123.31$

    Payout value of the put at expiration: 9/17/1999 (Strike price = 100) 1.045 @ -$ (intrinsic value)

    Payout value of the call at expiration: 9/17/1999 (Strike price = 118) 1.045 @ (8.63)$ (intrinsic value)

    Roll In 9 /17 /1999 Purchase QQQ 0.924 @ 126.63$ 123.31$

    Purchase a 6-month 2% OTM put ex pi ri ng on: 3/18/2000 (Strike pri ce = 124) 0.924 @ 10.25$ (at ask)

    Sell a 1-month 2% OTM call expiring on: 10/16/1999 (Strike price = 129) 0.924 @ (3.38)$ (at bid)

    Active Strategy Market Signals

    For the active implementations, a series of three market signals determine the choice of

    initial call and put moneyness, as well as the ratio of the number of calls written to the number of

    puts and QQQ shares purchased, while the time to expiration is fixed at one month for the calls

    and 6 months for the puts.

    Active Collar Adjustment Strategy: Three different sets of active market signals are used for the

    strategy implementations, differing by their time horizon; short, medium and long-term. The

    three signals are based on momentum, volatility and a compound macroeconomic indicator

  • 8/10/2019 Qqq Collar Study

    8/46

    8

    (unemployment claims and business cycle), respectively. In order to ensure that the strategies are

    investable, all signals use contemporaneously lagged data7.

    Momentum Signal: The momentum signal is a simple moving average cross-over (SMACO) of

    the NASDAQ-100 index (NDX)8. A SMACO compares a short-term moving average (SMA)

    and a long-term moving average (LMA) to determine whether an upward or downward trend

    exists. The rule is defined by the number of days covered by each of the moving averages. For

    example, a 5/150 SMACO rule compares a 5 day SMA with a 150 day LMA. If the SMA is

    greater (less) than the LMA, then an upward (downward) trend indicated, suggesting a buy (sell)

    signal. Our choice of signals is based on Szakmary, Davidson, Schwarz [1999] and Lento

    [2008]9, which both consider 1/50, 1/150, 5/150, 1/200 and 2/200 SMACO rules on the NDX.

    Szakmary et al apply NASDAQ index SMACOs as buy/sell signals for individual stocks for the

    period from 1973 to 199110. They find some significant excess returns, although their

    significance does not survive transactions costs. Similarly, Lento finds some significant

    forecasting abilities in the same SMACO rules on the NASDAQ at a 10-day lag over the period

    of 1995 to 2008. Following their methodology, we use 1/50, 5/150, and 1/200 SMACO rules on

    the NDX. This provides us with a short, medium and long-term momentum signal. Each roll

    date, we calculate the SMA and LMA for each of the three momentum rules and use them to

    generate the momentum signals. All else equal, if the calculation results in a buy signal, the

    7The signals are designed so that they are based only on data which existed prior to the date on which the

    signal would have been generated in practice. For example, a signal for the March 19, 1999 option roll-indate would only use data which existed on March 18, 1999 or earlier.8The use of the NDX rather than the QQQ provides us with historical data beyond the introduction of theQQQ. In this way, we can generate signals from the beginning of the QQQ data series.9Additional evidence of the existence of momentum and potential explanations for its existence can befound in Jegadeesh and Titman [2001] and Schneeweis, Kazemi and Spurgin [2008].10In this paper they do not take short positions. They use the signals as in/out position indicators.

  • 8/10/2019 Qqq Collar Study

    9/46

    9

    collar would widen (increasing upside participation with a corresponding reduction in downside

    protection). In contrast, all else equal, the collar would be tightened in response to sell signal

    (increasing downside protection while reducing upside participation).

    The following example illustrates the process for the momentum signal calculation:

    Momentum Signal Calculation for the 3/19/1999 Roll Date

    1 Day SMA 5 Day SMA 50 Day SMA 150 Day SMA 200 Day SMA

    2102.77 2061.98 1998.76 1629.73 1554.89

    Short Term Momentum Signal Calculation:

    1 Day SMA = 2102.77 >50 Day SMA = 1998.76

    Medium Term Momentum Signal Calculation:5 Day SMA = 2061.98 >150 Day SMA = 1629.73

    Long Term Momentum Signal Calculation:

    1 Day SMA = 2102.77 >200 Day SMA = 1554.89

    LONG NDX

    Momentum

    Signal

    MEDIUM NDX

    Momentum

    Signal

    SHORT NDX

    Momentum

    Signal

    +1 +1 +1

    Note: All moving averages using data up to the prior day's close (e .g. 3/18/1999)

    Since the 1 day SMA is greater than the 50 day SMA, the NDX is trending

    upwards. This is a bull ish s ignal, so the momentum signal = +1. Holding

    the macroeconomic s ignal constant, this would widen the collar (move

    the put 1% further OTM and the call 1% further OTM).

    Since the 5 day SMA is greater than the 50 day SMA, the NDX is trending

    upwards. This is a bull ish s ignal, so the momentum signal = +1. Holding

    the macroeconomic s ignal constant, this would widen the collar (move

    the put 1% further OTM and the call 1% further OTM).

    Since the 1 day SMA is greater than the 200 day SMA, the NDX is trending

    upwards. This is a bull ish s ignal, so the momentum signal = +1. Holding

    the macroeconomic s ignal constant, this would widen the collar (move

    the put 1% further OTM and the call 1% further OTM).

    Volatility Signal: The volatility signal is based on Renicker and Mallick [2005]. Renicker and

    Mallick create an enhanced S&P 500 buy-write strategy and back test it over the period from

    1997 to September 2005.11They find excess returns to a strategy which writes 0.75 calls to each

    long index position when the markets short-term anxiety level is high (as indicated by a situation

    11Note that since the Renicker and Mallick study reported results based on the period used in this study, the use ofthis variable is not independent from the period used to analze its impact on the collar strategy.

  • 8/10/2019 Qqq Collar Study

    10/46

    10

    in which the 1-month ATM S&P 500 implied volatility is more than 1 standard deviation above

    its current 250-day moving average level), and writes 1.25 calls per index position when the

    anxiety level is low (when the 1-month implied volatility is more than 1 standard deviation

    below the 250-day average level)12. Their goal in varying the quantity of written calls is to have a

    longer exposure to the market in times of high anxiety and shorter exposure in times of

    complacency. We make two minor modifications to their strategy. First, we use the daily VIX

    close as an indicator of implied volatility levels. Second, we consider a short, medium and long-

    term time frame to generate the 3 corresponding signals. In order to match the time frames of our

    momentum signals our short, medium and long-term volatility signals use 50, 150 and 250-day

    windows respectively. In keeping with the methodology of Renicker and Mallick, on roll dates

    we sell 0.75 (1.25) calls per index position when the previous days VIX close is more than 1

    standard deviation above (below) its current moving average level, otherwise we sell 1 call per

    index position as illustrated by the following formula:

    # of Calls Written per Long Put and Long QQQ Position = 1 + (0.25 * Volatility Signal),

    where the volatility signal is -1, 0 or +1.

    12When the 1-month implied volatility level is within the 1 standard deviation bounds, they follow astandard 1:1 ratio buy-write.

  • 8/10/2019 Qqq Collar Study

    11/46

    11

    Volatility Signal Calculation for the 3/19/1999 Roll Date

    Spot VIXVIX 250-Day Standard

    Deviation

    VIX 250-Day

    Moving Average

    VIX 150-Day Standard

    Deviation

    VIX 150-Day

    Moving Average

    VIX 50-Day Standard

    Deviation

    VIX 50-Day

    Moving Average

    24.3 6.5 27.0 5.9 30.4 2.5 27.8

    Short Term Volatili ty 1-Standard Deviation Range Calculation:1-Standard Deviation Range = VIX 50-Day Moving Average +/- VIX 50-Day Standard Deviation

    = 27.8 - 2.5 to 27.8 + 2.5

    = 25.3 to 30.3

    Medium Term Volatili ty 1-Standard Deviation Range Calculation:

    1-Standard Deviation Range = VIX 150-Day Moving Average +/- VIX 150-Day Standard Deviation

    = 30.4 - 5.9 to 30.4 + 5.9

    = 24.6 to 36.3

    Long Term Volatili ty 1-Standard Deviation Range Calculation:

    1-Standard Deviation Range = VIX 250-Day Moving Average +/- VIX 250-Day Standard Deviation

    = 27.0 - 6.5 to 27.0 + 6.5

    = 20.5 to 33.5

    VIX 50-Day 1 Std.

    Dev. Range

    VIX 150-Day 1 Std.

    Dev. Range

    VIX 250-Day 1 Std.

    Dev. Range

    25.3 to 30.3 24.6 to 36.3 20.5 to 33.5

    Short Term Momentum Signal Calculation:

    Medium Term Momentum Signal Calculation:

    Long Term Momentum Signal Calculation:

    LONG Volatility

    Signal

    MEDIUM Volatility

    Signal

    SHORT Volatility

    Signal

    0 +1 +1

    Note: Spot VIX level and all calculations use data up to the prior day's close (e.g. 3/18/1999)

    Spot VIX = 24.3

  • 8/10/2019 Qqq Collar Study

    12/46

    12

    Macroeconomic Signal: The final variable used in the active collar adjustment strategy signal

    process is based on the trend of initial unemployment claims and the state of the economy with

    respect to the business cycle. Boyd, Hu and Jagannathan [2005] consider the impact of

    unemployment rate surprise on the stock market in the period from 1973 to 2000. They find that

    in expansionary periods, stocks typically rise on bad unemployment news, while the opposite

    relationship holds in contractionary periods14. This is consistent with Veronesi [1999] which

    suggests that bad news in expansionary periods and good news in contractionary periods are

    typically correlated with an increase in uncertainty and an increase in the equity risk premium

    (corresponding to an increase in expected returns and reduction in current prices). We use these

    findings to construct a signal based on initial unemployment claims. The announcements from

    the NBERs Business Cycle Dating Committee are used to identify the state of the business

    cycle. It is worth noting that NBER does not define a recession as two consecutive quarters of

    negative GDP growth. They define it as follows: A recession is a significant decline in

    economic activity spread across the economy, lasting more than a few months, normally visible

    in real GDP, real income, employment, industrial production and wholesale-retail sales15. These

    announcements are generally considered the authority on the current state of the business cycle.

    Since there is often a significant delay in announcement dates, we base the signals on

    announcement dates to avoid hindsight biases. For example, the December 2007 peak was

    14These results are somewhat counter-intuitive in the case of expansionary economies. One might expectrising unemployment to negatively affect stock prices regardless of the business cycle, but the literaturecited above suggests that rising unemployment in expansionary economies causes expected future interestrates to decline, increasing the value of equities, while rising unemployment in contractions indicatesslower future earnings growth rates, reducing the value of equities.15See http://www.nber.org/cycles.html

  • 8/10/2019 Qqq Collar Study

    13/46

    13

    announced about one year later on December 1, 2008. Our signal would be based on an

    expansionary economy until December 1, 2008. Since initial unemployment claims are released

    on a weekly basis, we include a one-week lag in the calculations to ensure the investability of our

    strategy. In order to closely match the macroeconomic signal methodology with those of the

    momentum and volatility signals, we base our short, medium and long-term macroeconomic

    signals on 1/10, 1/30 and 1/40 week SMACOs for weekly initial unemployment claims. Since

    rising unemployment claims in an expansionary economy is a bullish stock market price and

    volatility signal, if the SMA is greater than the LMA, we shift the collar towards the ATM put

    and OTM call (increasing both strike prices) thereby increasing the portfolios exposure to

    upside moves as well as increasing its vega16. In contractionary periods, rising unemployment

    claims would cause us to shift the strike prices in the opposite direction.

    16Since vega is highest for ATM options, moving the short call further OTM and moving the long puttowards the ATM will increase the vega of both option positions.

  • 8/10/2019 Qqq Collar Study

    14/46

    14

    These calculations can be illustrated with the following example:

    Macroeconomic Signal Calculation for the 3/19/1999 Roll Date

    NBER Announcements

    Date Indication12/22/1992 Trough

    11/26/2001 Peak (3/19/1999 is during an expansionary economy)

    So on 3/19/1999, a downward trend in unemployment is a bearish signal.

    1 Week SMA 40 Week SMA 30 Week SMA10 Week

    SMA

    LONG

    Unemployment

    Trend

    MEDIUM

    Unemployment

    Trend

    SHORT

    Unemployment

    Trend

    308.0 317.1 311.8 311.4 Down Down Down

    Short Term Macroeconomic Signal Calculation:

    1 Week SMA = 308.0

  • 8/10/2019 Qqq Collar Study

    15/46

    15

    date, the initial moneyness of the puts and calls is determined based on the momentum and

    macroeconomic signals and the ratio of written calls is determined by the volatility signal. Our

    rules are constructed in such a manner to ensure that the target initial percentage moneyness of

    the options will be an integer which falls between ATM and 5% OTM. The signals adjust the

    initial moneyness of the puts and calls from a level near the center of the range at 3% OTM and

    2% OTM, respectively18. From this central point, the momentum signal will serve to widen or

    tighten the collar by increasing or decreasing the amount OTM, respectively. The

    macroeconomic signal will shift the collar up by increasing the amount OTM of the calls and

    decreasing the amount OTM of the puts, or shift the collar down by moving the strikes in the

    opposite direction. The net effect can be illustrated by the following formulas for the call strikes:

    Call % OTM = 2 + (Momentum signal + Macroeconomic signal),

    and for puts:

    Put % OTM = 3 + (Momentum signal - Macroeconomic signal),

    where the momentum signal and the macroeconomic signal are +1/-1 binary signals.

    The following example provides an illustration of the trading signal calculation:

    18Puts tend to cost more than calls for a given level of moneyness, so we start the puts further OTM toallow the option component of the strategy to be close to zero cost.

  • 8/10/2019 Qqq Collar Study

    16/46

    16

    Trading Rule Calculation Based on the Three Signals for the 3/19/1999 Roll Date

    Short Term Trading Rule Calculation:

    Initial Call Moneyness = 2% OTM + (Momentum signal + Macroeconomic signal) = (2+1-1)% OTM = 2% OTM

    Initial Put Moneyness = 3% OTM + (Momentum signal - Macroeconomic signal) = (3+1+1)% OTM = 5% OTM

    Number of Calls per Put and QQQ Positi on = 1.00 + (0.25 * Volatil ity Signal ) = 1 + (0.25 * 1) = 1.25 Call s

    SHORT

    Macroeconomic

    Signal

    SHORT NDX

    Momentum

    Signal

    Call % OTM Put % OTM

    SHORT

    Volatility

    Signal

    QQQ/Put/Call

    Ratio

    -1 1 2 % OTM 5 % OTM 1 1/1/1.25

    Medium Term Trading Rule Calculation:

    Initial Call Moneyness = 2% OTM + (Momentum signal + Macroeconomic signal) = (2+1-1)% OTM = 2% OTM

    Initial Put Moneyness = 3% OTM + (Momentum signal - Macroeconomic signal) = (3+1+1)% OTM = 5% OTM

    Number of Calls per Put and QQQ Positi on = 1.00 + (0.25 * Volatil ity Signal ) = 1 + (0.25 * 1) = 1.25 Call s

    MEDIUM

    Macroeconomic

    Signal

    MEDIUM NDX

    Momentum

    Signal

    Call % OTM Put % OTM

    MEDIUM

    Volatility

    Signal

    QQQ/Put/Call

    Ratio

    -1 1 2 % OTM 5 % OTM 1 1/1/1.25

    Long Term Trading Rule Calculation:

    Initial Call Moneyness = 2% OTM + (Momentum signal + Macroeconomic signal) = (2+1-1)% OTM = 2% OTM

    Initial Put Moneyness = 3% OTM + (Momentum signal - Macroeconomic signal) = (3+1+1)% OTM = 5% OTM

    Number of Calls per Put and QQQ Positi on = 1.00 + (0.25 * Volatil ity Signal ) = 1 + (0.25 * 0) = 1.00 Call s

    LONG

    Macroeconomic

    Signal

    LONG NDX

    Momentum

    Signal

    Call % OTM Put % OTM

    LONG

    Volatility

    Signal

    QQQ/Put/Call

    Ratio

    -1 1 2 % OTM 5 % OTM 0 1/1/1

    The trading rules which result from the signals are provided in Exhibit 1. The frequency

    distributions of the strike prices and call writing ratios are provided in Exhibit 2.

    Exhibit 1: Trading Rules

    NDX Momentum

    Signal

    Macroeconomic

    signal

    Call %OTM =

    2 + (Momentum Signal +

    Macroeconomic Signal)

    Put %OTM =

    3 + (Momentum Signal -

    Macroeconomic Signal)

    Call Initial

    % OTM

    Put Initial

    % OTM

    Scenario 1 -1 -1 = 2 - 1 - 1 = 3 - 1 - (-1) 0% 3%

    Scenario 2 +1 -1 = 2 + 1 - 1 = 3 + 1 - (-1) 2% 5%

    Scenario 3 -1 +1 = 2 - 1 + 1 = 3 - 1 - (+1) 2% 1%

    Scenario 4 +1 +1 = 2 + 1 + 1 = 3 + 1 - (+ 1) 4% 3%

    V IX S igna l QQQ/ C all Ra tio

    Scenario 1 -1 1.0/0.75

    Scenario 2 0 1.0/1.0

    Scenario 3 1 1.0/1.25

  • 8/10/2019 Qqq Collar Study

    17/46

    17

    Exhibit 2: Trading Rule Frequency Distributions

    Initial % OTMCall Moneyness

    Frequency

    Put Moneyness

    Frequency

    Call Moneyness

    Frequency

    Put Moneyness

    Frequency

    Call Moneyness

    Frequency

    Put Moneyness

    Frequency

    ATM 20% 0% 16% 0% 15% 0%

    1% OTM 0% 29% 0% 24% 0% 34%

    2% OTM 58% 0% 65% 0% 69% 0%

    3% OTM 0% 29% 0% 41% 0% 17%

    4% OTM 22% 0% 19% 0% 15% 0%

    5% OTM 0% 41% 0% 34% 0% 49%

    QQQ/ Call RatioCall Ratio

    Frequency

    Call Ratio

    Frequency

    Call Ratio

    Frequency

    1.0/ 0.75 20% 21% 20%

    1.0/ 1.0 45% 42% 48%

    1.0/ 1.25 36% 37% 32%

    Short-T erm Signa ls Medium-T erm Signa ls Long-T erm Signals

    In a later section of the paper we also apply an active and passive collar to a typical small

    cap mutual fund. Since the beta of a fund will not necessarily be 1.0 with respect to the QQQ and

    the price level of the fund will not match the QQQ underlying price, we scale the option

    positions by the 65-day rolling 1 day lagged beta as well as by the relative price levels of the

    fund and the QQQ. To adjust for the relative price levels, each day we rebalance our portfolio so

    that the ratio of the number of options to the number of shares of the fund is equal to beta times

    the ratio of the mutual fund price over the QQQ price, as given by the following formula19:

    # of puts or calls = Betamutual fund, QQQ * Pricemutual fund/PriceQQQ

    19For active strategies, we also apply the call ratio adjustment based on the volatility signal.

  • 8/10/2019 Qqq Collar Study

    18/46

    18

    This process allows us to maintain the equivalent of a 1:1:1 ratio collar. While the beta is

    set at each roll date, the relative balance due to price changes is reset each day20. For example, if

    the rolling beta of the mutual fund is 0.75, the price of the mutual fund is $20 and the price of the

    QQQ is $60 on the roll in date, we write 0.25 calls and purchase 0.25 puts for each long position

    in the mutual fund, and rebalance each day (using the 0.75 beta and the current prices) until the

    expiration of the options at which time we rebalance using the new rolling beta level as well as

    the current prices. The following example provides an illustration of the process by which we

    generate the passive mutual fund collar:

    Passive 2% OTM 1-Month Call 6-Month Put Mutual Fund Collar Implementation

    Date Exdate Quantity Wealth

    65-Day

    Rolling

    Beta with

    QQQ

    Price of

    Mutual

    Fund

    Price of

    QQQ

    Mutual

    Fund:Put:

    Call Ratio

    Roll In 3/19 /1999 Purchase mutual fund 1.0000 @ 99.36$ 101.76$ ( In it ial ) 0. 396 99. 355 102. 437 1:0. 38:0. 38

    Purch as e a 6- mo nt h 2% OTM QQQ pu t e xp ir in g o n: 9/17/ 1999 ( St rike pr ice = 100) 0.3840 @ 9.50$ (at ask)

    S el l a 1- mo nt h 2% OT M QQ Q ca ll ex pi ri ng on : 4/ 16/ 1999 ( St ri ke pr ic e = 104) 0. 3840 @ ( 3. 25)$ (at bid)

    Value 3/22 /1999 Value of of mutual fund 1.0000 @ 99.17$ 101.88$

    Value of of QQQ puts 9/17/1999 (Strike price = 100) 0.3840 @ 9.69$ (mid of bid/ask)

    Value of of QQQ calls 4/16/1999 (Strike price = 104) 0.3840 @ (2.63)$ (mid of bid/ask)

    Rebalance 3/22 /1999 Adjust quantities to maintain the ratio using current prices and the 3/19/1999 beta of 0.396

    Adjust quantity of mutual fund 0.9997 @ 99.17$ 101.88$ 99.171 101.187 1:0.39:0.39

    Adjust quantity of QQQ puts 9/17/1999 (Strike price = 100) 0.3880 @ 9.69$ (mid of bid/ask)

    Adjust quantity of QQQ calls 4/16/1999 (Strike price = 104) 0.3880 @ (2.63)$ (mid of bid/ask)

    Roll Out 4/16 /1999 Mutual fund value 0.9988 @ 112.34$ 115.71$ 112.339 107.062 1:0.42:0.42

    K ee p t he pu t ( no w 5-m on th 4% OTM) e xp ir in g o n: 9/17/ 1999 ( St rike pr ice = 100) 0.41543 @ 8.44$ (mid of bid/ask)

    P ayout val ue of pre vi ous cal l at ex pi rati on: 4/16/1999 ( Stri ke pri ce = 104) 0.41543 @ -$ (intrinsic value)

    Roll In 4/16 /1999 Since this i s a roll date, adjust quantiti es to the new 4/16/1999 beta of 0.340

    Keep the mutual fund 1.015 @ 112.34$ 115.71$ 0.340 112.339 103.937 1:0.37:0.37

    K ee p t he p ut ( no w 5-m on th 4% O TM) e xp ir in g o n: 9/17/ 1999 ( St rike p rice = 100) 0.373 @ 8.44$ (mid of bid/ask)

    S el l a 1- mo nt h 2% OT M QQ Q ca ll e xp ir in g on : 5/ 22/ 1999 ( St ri ke pr ic e = 106) 0. 373 @ ( 4. 00)$ (at bid)

    Repeat until put expires, each day between roll dates rebalance quantities to the beta calculated on the previous roll date

    Roll Out 9/17 /1999 Mutual fund value 0.966 @ 146.04$ 145.61$ 0.469 146.041 126.625

    Payout value of the put at expiration: 9/17/1999 (Strike price = 100) 0.523 @ -$ (intrinsic value)

    Payout value of the call at expiration: 9/17/1999 (Strike price = 118) 0.523 @ 8.63$ (intrinsic value)

    Roll In 9/17 /1999 Keep the mutual fund 0.972 @ 146.04$ 145.61$

    Purch as e a 6- mo nt h 2% OTM QQQ pu t e xp ir in g o n: 3/18/ 2000 ( St rike pr ice = 124) 0.526 @ 10.25$ (at ask)

    S el l a 1- mo nt h 2% OT M QQ Q ca ll ex pi ri ng on : 10/ 16/ 1999 ( St ri ke pr ic e = 129) 0. 526 @ ( 3. 38)$ (at bid)

    20Beta is reset only on roll dates to closely match the methodology of the passive collar strategies to themethodology of active collar strategies.

  • 8/10/2019 Qqq Collar Study

    19/46

    19

    Trading Rule Calculation For Mutual Fund Collar

    Short Term Trading Rule Calculation:

    Initial Call Moneyness = 2% OTM + (Momentum signal + Macroeconomic signal) = (2+1-1)% OTM = 2% OTM

    Initial Put Moneyness = 3% O TM + (Momentum signal - Macroeconomic signal) = (3+1+1)% OTM = 5% OTM

    Number of Calls and Puts per Mutual Fund Position before Volatility Signal Impact = Beta Mutual Fund, QQQ* PriceMutual Fund/PriceQQQ

    Number of Calls and Puts per Mutual Fund Position before Volatility Signal Impact = 0.396 * 99.36 / 102.44 = 0.38

    Volatility Signal Impact:

    Number of Calls per Put = 1.00 + (0.25 * Volatility Signal) = 1 + (0.25 * 1) = 1.25 Calls/Put

    Number of Puts per Mutual Fund Position = 0.38

    Number of Calls per Mutual Fund Position = 1.25 * 0.38 = 0.48

    SHORT

    Macroeconomic

    Signal

    SHORT NDX

    Momentum

    Signal

    Cal l % OTM Put % OTM

    SHORT

    Volatility

    Signal

    65-Day

    Rolling

    Beta with

    QQQ

    Price of

    Mutual

    Fund

    Price of

    QQQ

    Mutual Fund/Put/Call

    Ratio

    -1 +1 2 % OTM 5 % OTM 1 0.396 99.36 102.44 1/0.38/0.48

    Medium Term Trading Rule Calculation:

    Initial Call Moneyness = 2% OTM + (Momentum signal + Macroeconomic signal) = (2+1-1)% OTM = 2% OTM

    Initial Put Moneyness = 3% O TM + (Momentum signal - Macroeconomic signal) = (3+1+1)% OTM = 5% OTM

    Number of Calls and Puts per Mutual Fund Position before Volatility Signal Impact = Beta Mutual Fund, QQQ* PriceMutual Fund/PriceQQQ

    Number of Calls and Puts per Mutual Fund Position before Volatility Signal Impact = 0.396 * 99.36 / 102.44 = 0.38

    Volatility Signal Impact:

    Number of Calls per Put = 1.00 + (0.25 * Volatility Signal) = 1 + (0.25 * 1) = 1.25 Calls/Put

    Number of Puts per Mutual Fund Position = 0.38

    Number of Calls per Mutual Fund Position = 1.25 * 0.38 = 0.48

    MEDIUM

    Macroeconomic

    Signal

    MEDIUM NDX

    Momentum

    Signal

    Cal l % OTM Put % OTM

    MEDIUM

    Volatility

    Signal

    65-Day

    Rolling

    Beta with

    QQQ

    Price of

    Mutual

    Fund

    Price of

    QQQ

    Mutual Fund/Put/Call

    Ratio

    -1 +1 2 % OTM 5 % OTM 1 0.396 99.36 102.44 1/0.38/0.48

    Long Term Trading Rule Calculation:

    Initial Call Moneyness = 2% OTM + (Momentum signal + Macroeconomic signal) = (2+1-1)% OTM = 2% OTM

    Initial Put Moneyness = 3% O TM + (Momentum signal - Macroeconomic signal) = (3+1+1)% OTM = 5% OTM

    Number of Calls and Puts per Mutual Fund Position before Volatility Signal Impact = Beta Mutual Fund, QQQ* PriceMutual Fund/PriceQQQ

    Number of Calls and Puts per Mutual Fund Position before Volatility Signal Impact = 0.396 * 99.36 / 102.44 = 0.38

    Volatility Signal Impact:

    Number of Calls per Put = 1.00 + (0.25 * Volatility Signal) = 1 + (0.25 * 0) = 1.00 Calls/Put

    Number of Puts per Mutual Fund Position = 0.38

    Number of Calls per Mutual Fund Position = 1.00 * 0.38 = 0.38

    LONG

    Macroeconomic

    Signal

    LONG NDX

    Momentum

    Signal

    Cal l % OTM Put % OTM

    LONG

    Volatility

    Signal

    65-Day

    Rolling

    Beta withQQQ

    Price of

    Mutual

    Fund

    Price of

    QQQ

    Mutual Fund/Put/Call

    Ratio

    -1 +1 2 % OTM 5 % OTM 0 0.396 99.36 102.44 1/0.38/0.38

    Results

    Before reviewing the results of the passive and active approach to collar protection, it is

    perhaps important to briefly discuss three issues in option based risk management:

    1) The use of alternative approaches to protecting equity investments,

  • 8/10/2019 Qqq Collar Study

    20/46

    20

    2) the impact of option based strategies on traditional forms of risk comparisons (e.g. Sharpe

    Ratio), and

    3) the necessity for analyzing results over alternative time periods.

    Alternative Approaches to Option Based Risk Management: There are alternative option based

    approaches to protecting equity based investments. The most obvious choice is typically the use

    of protective puts. Unfortunately, the use of protective puts tends to be a relatively expensive

    method of capital protection, especially in periods of high volatility. The existence of a negative

    volatility risk premium and the resulting excess returns associated with put writing are indicative

    of the potential cost of purchasing protective puts21. Another option based approach is the buy-

    write or covered call strategy. The covered call strategy typically entails the writing of call

    options against a long underlying index position at a one-to-one ratio. A number of studies have

    suggested that covered call writing can provide return enhancement as well as a cushion to

    mitigate losses from market downturns. These include Schneeweis and Spurgin [2001], Whaley

    [2002] and Hill et al [2006] which apply the strategy to the S&P 500 and Kapadia and Szado

    [2007] which applies the buy-write to a broader index, the Russell 2000. Unfortunately, covered

    call writing still leaves an investor exposed to large down moves.

    Impact of Option Use on Traditional Risk Measures: It should also be noted that we have

    included Sharpe ratios with our other performance measures for the sake of consistency with

    previous literature, but great care should be taken in interpreting the Sharpe ratios. First, a

    21The richness of put prices is not without controversy. While a great deal of literature supports optionrichness (particularly for put options), extensive literature debates its existence (for example, see Ungarand Moran [2009] and Bakshi and Kapadia [2003]).

  • 8/10/2019 Qqq Collar Study

    21/46

    21

    number of the calculated Sharpe ratios are negative. Negative Sharpe ratios are uninformative.

    Second, even with positive excess returns, traditional risk-adjusted performance measures such

    as the Sharpe ratio and Jensens alpha can be misleading. This is particularly true for portfolios

    which include option strategies or other strategies which may result in skewed or kurtotic return

    distributions. The Sharpe ratio and Jensens alpha assume normally distributed returns22. In

    recognition of the fact that the return distributions generated by our collar strategies may be non-

    normal, we utilize the Stutzer index and Lelands alpha as measures of risk adjusted

    performance. These measures adjust for the fact that investors which exhibit non-increasing

    absolute risk aversion prefer positive skewness

    23

    . Therefore positively skewed return

    distributions should exhibit lower expected returns than negatively skewed distributions, ceteris

    paribus.

    Alternative Time Period Analysis: This paper does not assume any particular model of investor

    risk aversion. The significance of the results for any particular investor may therefore be

    dependent on that investors individual risk tolerance. Results should therefore be presented over

    various market conditions which provide investors a wider range of results consistent with a

    particular risk environment. In order to assess the performance and risk management

    characteristics of the passive and active collar strategies in different market environments, we

    break up our time period into 3 sub-periods.

    The first sub-period is April 1999 to September 2002. We would expect that this would

    be a relatively favorable period for the collar strategy, when compared to holding a long index

    22It is also quite possible to manipulate the Sharpe ratio. For example, see Spurgin [2001].23See Arditti [1967].

  • 8/10/2019 Qqq Collar Study

    22/46

    22

    position. In this period the QQQ exhibited extremely high realized volatility and experienced a

    rapid loss of more than of its value from peak to trough. While one would expect that

    protective strategies would be very beneficial with a drop of this magnitude, there are two factors

    that mitigate the benefits of the protective puts. First, put options would likely be very expensive

    in this environment. Secondly, the short call position would greatly limit the upside participation

    of the collar in the incredibly strong run-up of the early part of the sub-period. This is a

    particularly interesting sub-period to study, because it captures the run-up and collapse of a

    bubble in the underlying.

    The second sub-period, which covers October 2002 to September 2007, is less favorable

    for the collar strategy. In fact, one might argue that this time period is representative of nearly

    the worst environment for the collar (when compared to a long underlying position). In this

    period, the QQQ exhibits a steady growth rate with relatively low volatility24and few sharp

    downward moves. In this environment, the collar may lose significant revenue on the upside due

    to the short calls while it gains very little from the protective puts.

    The final sub-period covers October 2007 to May 2009. This is another favorable period

    for the collar and covers a major financial crisis which negatively impacted most asset classes.

    Unlike the first sub-period, this favorable period does not include a strong run-up in the

    underlying. Thus we have two relatively favorable sub-periods to consider (one that covers the

    tech bubble and one that covers the credit crisis) as well as one clearly unfavorable sub-period.

    Before discussing the performance of the collar strategies, it is worth noting that the 1-

    month/6-month and 1-month/3-month strategies require rebalancing each month in order to

    24The 17.5% volatility in this sub-period is quite high, but much smaller than the 30% volatility of theoverall period or the 42% of the early sub-period.

  • 8/10/2019 Qqq Collar Study

    23/46

    23

    reinvest the funds that are collected from the sale of the calls and the funds that are disbursed to

    cover the cost of calls that expire ITM between put expirations. No adjustment is made for the

    transactions costs that would be incurred by these rebalancing activities.

    Exhibit 3: Growth of $100 in QQQ March 1999 to May 2009

    $0.00

    $50.00

    $100.00

    $150.00

    $200.00

    $250.00

    Mar-99

    Sep-99

    Mar-00

    Sep-00

    Mar-01

    Sep-01

    Mar-02

    Sep-02

    Mar-03

    Sep-03

    Mar-04

    Sep-04

    Mar-05

    Sep-05

    Mar-06

    Sep-06

    Mar-07

    Sep-07

    Mar-08

    Sep-08

    Mar-09

    QQQ TR Growth of $100

  • 8/10/2019 Qqq Collar Study

    24/46

    24

    Empirical Results

    Passive Collars: We first consider the performance of passive collar strategies. Our discussion is

    centered on 1-month call/6-month put collar strategies25. Results comparing the 1-month call/6-

    month put collars to the 1-month call/1-month put collars are provided in Appendix B.

    While the exhibits provide statistics for a wide range of collar implementations, our discussion is

    focused on the 2% OTM strategies, since they represent a middle ground between the ATM and

    the far OTM strategies. Exhibits 4a, 4b, 4c and 4d provide summary statistics for passive 1-

    month call/6-month put collar strategies utilizing 2% OTM puts with ATM to 5% OTM calls for

    the full period as well as the three sub-periods. Similarly, Exhibits 5a, 5b, 5c and 5d provide

    summary statistics for 2% OTM call collars which use ATM to 5% OTM puts. It is immediately

    apparent when reviewing the exhibits that, while the performance characteristics of the strategy

    are sensitive to the choice of moneyness for the options, they are far more sensitive to the market

    environment (rising and/or falling) in which the strategy is implemented. In contrast, the choice

    of time to maturity for the calls of 1-month versus 6-month can have a far more significant

    impact, as evidenced by the results provided in Appendix B.

    The summary statistics for the overall period are provided in Exhibits 4a and 5a. Over the

    122 months of the study, the 2% OTM collar significantly reduces risk and improves realized

    returns. The returns are improved from a -3.6% annualized loss to a 9.3% gain, meanwhile

    standard deviation is reduced by about 1/3 from 30.4% to 11.0%. Similarly, the sign of the

    Stutzer index is turned from negative to positive, and the information ratio (relative to the QQQ)

    for the collar is positive at 0.45. Perhaps the most visible impact of implementing the collar

    25Previous research indicates that these strategies have typically outperformed 1-month call/1-month putstrategies in the recent past. See, for example Szado and Kazemi [2008].

  • 8/10/2019 Qqq Collar Study

    25/46

    25

    strategy is a reduction of the maximum drawdown from -81.1% to -17.9% for the 10+ year

    overall period.

    Exhibit 4a Passive Collars with 2% OTM PutsApril 1999 to May 2009

    Mo nthly Data: April, 1999-

    Ma y, 2009

    QQQQ TR

    FUND ONLY -

    No Opt ions

    QQQQ TR PASSIVE

    COLLAR - 0% OTM, 1

    Mo Ca l l .2% OTM. 6

    M o P u t .

    QQQQ TR PASSIVE

    COLLAR - 1% OTM, 1M o

    Ca l l .2% OTM . 6 Mo Put .

    QQQQ TR PASSIVE

    COLLAR - 2% OTM, 1M o

    Ca l l .2% OTM . 6 Mo Put .

    QQQQ TR PASSIVE

    COLLAR - 3% OTM, 1M o

    Ca l l .2% OTM . 6 Mo Put .

    QQQQ TR PASSIVE

    COLLAR - 4% OTM, 1M o

    Ca l l .2% OTM . 6 Mo Put .

    QQQQ TR PASSIVE

    COLLAR - 5% OTM, 1M o

    Ca l l .2% OTM . 6 Mo Put .

    Annualized Return -3.57% 10.69% 9.12% 9.26% 9.23% 8.84% 7.61%

    Annualized Std Dev 30.40% 9.86% 10.45% 10.98% 11.54% 11.94% 12.37%

    Sharpe Ratio -0.22 0.77 0.58 0.56 0.53 0.48 0.37

    Annual Stutzer Index -0.07 0.79 0.60 0.59 0.57 0.52 0.41

    C A P M B e t a 1.00 0.02 0.11 0.13 0.17 0.21 0.23

    Leland Beta 1.00 0.01 0.10 0.13 0.17 0.20 0.23

    Mo nthly Leland Alpha 0.00% 0.64% 0.54% 0.56% 0.57% 0.55% 0.46%

    Information Ratio 0.00 0.45 0.44 0.45 0.47 0.47 0.44

    Skew -0.21 0.45 0.18 0.16 0.14 0.09 0.03

    Kurtosis 0.55 2.75 3.34 3.52 3.51 2.95 2.99

    Maximum Drawdown -81.08% -14.21% -17.08% -17.90% -19.49% -20.14% -21.37%

    Correlation with QQQ 1.00 0.05 0.31 0.37 0.46 0.52 0.57

    Min M onth ly Re tur n -26.20% -8.15% -9.29% -9.95% -10.10% -10.67% -10.73%

    Max Mo nthly Return 23.48% 12.81% 14.09% 15.06% 15.48% 15.37% 15.64%

    Number of Months 122 122 122 122 122 122 122

    % Up M onths 52% 67% 63% 65% 67% 62% 60%

    % Down Months 48% 33% 37% 35% 33% 38% 40%

    The effectiveness of the collar strategy in the April 1999 to September 2002 is evident in

    the results provided in Exhibit 4b and 5b. In the early bubble run-up and collapse, the QQQ

    experienced an annualized return of -23.3% with a 42% volatility. In this volatile market, the 2%

    OTM passive collar strategy generated an annualized return of 21.2% at a volatility of only

    13.7%. Thus the collar was able to turn a sizeable loss into a significant gain, while cutting risk

    (as measured by standard deviation) by more than 2/3. Other measures confirm the risk reduction

    including the minimum monthly return, the percentage of up months, and the Leland beta. The

    capital protection ability of the collar strategy can be illustrated by the maximum drawdown. The

    maximum drawdown of the QQQ is reduced significantly from -81.1% to -7.5% over the most

    severe market move that the QQQ has ever experienced.

  • 8/10/2019 Qqq Collar Study

    26/46

    26

    Exhibit 4b Passive Collars with 2% OTM PutsApril 1999 to September 2002

    Mo nthly Data: Apr. 1999-Sept,

    2002

    QQQQ TR

    FUND ONLY -

    No Options

    QQQQ TR PASSIVE

    COLLAR - 0% OTM, 1

    Mo Ca l l .2% OTM. 6

    M o P u t .

    QQQQ TR PASSIVE

    COLLAR - 1% OTM, 1M o

    Ca l l .2% OTM . 6 Mo Put .

    QQQQ TR PASSIVE

    COLLAR - 2% OTM, 1M o

    Ca l l .2% OTM . 6 Mo Put .

    QQQQ TR PASSIVE

    COLLAR - 3% OTM, 1M o

    Ca l l .2% OTM . 6 Mo Put .

    QQQQ TR PASSIVE

    COLLAR - 4% OTM, 1M o

    Ca l l .2% OTM . 6 Mo Put .

    QQQQ TR PASSIVE

    COLLAR - 5% OTM, 1M o

    Ca l l .2% OTM . 6 Mo Put .

    Annualized Return -23.31% 26.02% 21.66% 21.16% 19.43% 17.85% 15.85%

    Annualized Std Dev 42.44% 12.94% 13.27% 13.69% 14.33% 14.50% 14.91%

    Sharpe Ratio -0.65 1.69 1.32 1.24 1.07 0.95 0.79

    Annual Stutzer Index -0.51 1.58 1.27 1.21 1.06 0.96 0.81C A P M B e t a 1.00 0.00 0.06 0.08 0.11 0.14 0.16

    Leland Beta 1.00 0.00 0.06 0.08 0.12 0.14 0.16

    Mo nthly Leland Alpha 0.00% 1.67% 1.50% 1.50% 1.44% 1.37% 1.28%

    Information Ratio 0.00 1.11 1.08 1.08 1.07 1.06 1.04

    Skew 0.14 0.17 0.26 0.39 0.43 0.41 0.40

    Kurtosis -0.70 0.87 2.00 2.47 2.78 2.51 2.80

    Maximum Drawdown -81.08% -5.28% -7.54% -7.54% -9.16% -9.16% -10.39%

    Correlation with QQQ 1.00 0.00 0.21 0.27 0.34 0.41 0.47

    Min M onthly Return -26.20% -5.28% -7.54% -7.54% -9.16% -9.16% -10.39%

    Max M onthly Return 23.48% 12.81% 14.09% 15.06% 15.48% 15.37% 15.64%

    Number of Mo nths 42 42 42 42 42 42 42

    % Up Months 40% 74% 71% 74% 74% 67% 64%

    % Down Months 60% 26% 29% 26% 26% 33% 36%

    Exhibit 4c Passive Collars with 2% OTM PutsOctober 2002 to September 2007

    Monthly Data: Sept, 2002 to

    Sept. 2007

    QQQQ TR

    FUND ONLY -

    No Options

    QQQQ TR PASSIVE

    COLLAR - 0% OTM, 1

    Mo Call.2% OTM . 6

    Mo Put.

    QQQQ TR PASSIVE

    COLLAR - 1% OTM, 1 Mo

    Call.2% OTM . 6 Mo Put.

    QQQQ TR PASSIVE

    COLLAR - 2% OTM, 1 Mo

    Call.2% OTM . 6 Mo Put.

    QQQQ TR PASSIVE

    COLLAR - 3% OTM, 1 Mo

    Call.2% OTM . 6 Mo Put.

    QQQQ TR PASSIVE

    COLLAR - 4% OTM, 1 Mo

    Call.2% OTM . 6 Mo Put.

    QQQQ TR PASSIVE

    COLLAR - 5% OTM, 1 Mo

    Call.2% OTM . 6 Mo Put.

    Annualized Return 20.37% 3.73% 4.57% 5.19% 6.88% 7.42% 6.14%

    Annualized Std Dev 17.54% 5.58% 7.08% 7.93% 8.55% 9.14% 9.75%

    Sharpe Ratio 1.00 0.15 0.24 0.29 0.47 0.50 0.33

    Annual Stutzer Index 1.01 0.17 0.26 0.32 0.49 0.52 0.37

    C A P M B e ta 1.00 0.07 0.26 0.30 0.38 0.43 0.48

    Leland Beta 1.00 0.09 0.28 0.33 0.40 0.44 0.50

    Mo nthly Leland Alpha 0.00% -0.04% -0.24% -0.26% -0.23% -0.24% -0.42%

    Information Ratio 0.00 -0.96 -1.11 -1.12 -1.10 -1.15 -1.36

    Skew 0.33 -0.13 -0.21 -0.22 -0.25 -0.02 -0.20

    Kurtosis 1.63 0.24 0.03 0.04 -0.05 -0.07 0.37

    Ma ximum Drawdown -12.36% -6.62% -11.83% -14.02% -12.12% -14.33% -16.45%

    Correlation with QQQ 1.00 0.20 0.63 0.67 0.77 0.82 0.86

    Min M onthly Return -12.09% -3.67% -4.67% -5.49% -5.49% -5.50% -6.90%

    Max M onthly Return 18.47% 4.46% 4.88% 5.59% 5.91% 6.86% 6.86%

    Number of Months 60 60 60 60 60 60 60

    % Up Months 62% 65% 57% 57% 62% 60% 58%

    % Down Months 38% 35% 43% 43% 38% 40% 42%

    Exhibit 4d Passive Collars with 2% OTM PutsOctober 2007 to May 2009

    Mo nthly Data: Sept, 2007 to

    Ma y. 2009

    QQQQ TR

    FUND ONLY -

    No Opt ions

    QQQQ TR PASSIVE

    COLLAR - 0% OTM, 1

    Mo Ca l l .2% OTM. 6

    M o P u t .

    QQQQ TR PASSIVE

    COLLAR - 1% OTM, 1M o

    Ca l l .2% OTM . 6 Mo Put .

    QQQQ TR PASSIVE

    COLLAR - 2% OTM, 1M o

    Ca l l .2% OTM . 6 Mo Put .

    QQQQ TR PASSIVE

    COLLAR - 3% OTM, 1M o

    Ca l l .2% OTM . 6 Mo Put .

    QQQQ TR PASSIVE

    COLLAR - 4% OTM, 1M o

    Ca l l .2% OTM . 6 Mo Put .

    QQQQ TR PASSIVE

    COLLAR - 5% OTM, 1M o

    Ca l l .2% OTM . 6 Mo Put .

    Annualized Return -19.78% 2.44% -1.33% -1.44% -3.35% -4.20% -3.93%

    Annualized Std Dev 29.23% 10.46% 11.00% 11.56% 12.15% 12.92% 13.29%

    Sharpe Ratio -0.73 0.10 -0.25 -0.25 -0.39 -0.44 -0.40

    Annual Stutzer Index -0.67 0.15 -0.20 -0.20 -0.35 -0.40 -0.36

    C A P M B e t a 1.00 0.13 0.21 0.25 0.27 0.32 0.34

    Leland Beta 1.00 0.12 0.20 0.24 0.27 0.31 0.34

    Mo nthly Leland Alpha 0.00% 0.31% 0.14% 0.20% 0.08% 0.09% 0.16%

    Information Ratio 0.00 0.81 0.74 0.77 0.71 0.71 0.75

    Skew -0.16 -0.95 -1.53 -1.64 -1.47 -1.34 -1.36

    Kurtosis -0.88 2.18 2.74 3.08 2.43 2.12 2.00

    Maximum Drawdown -49.74% -14.21% -17.08% -17.90% -19.49% -20.14% -21.37%

    Correlation with QQQ 1.00 0.35 0.56 0.62 0.65 0.71 0.76

    Min M onth ly Re tur n -15.57% -8.15% -9.29% -9.95% -10.10% -10.67% -10.73%

    Max Mo nthly Return 13.06% 5.64% 3.84% 3.84% 4.65% 5.26% 5.39%

    Number of Months 20 20 20 20 20 20 20

    % Up M onths 50% 60% 65% 70% 70% 60% 55%

    % Down Months 50% 40% 35% 30% 30% 40% 45%

    To consider these results in a different light, the collar could have earned an investor

    21.2% per year over the period with a maximum loss of capital of 7.5% regardless of how poorly

  • 8/10/2019 Qqq Collar Study

    27/46

    27

    the investor timed their entry into the strategy. Clearly in this case, the collar was an effective

    way of capturing a significant return from the bubble run-up without experiencing the magnitude

    of losses that came with the collapse.

    We expected the collar to perform poorly in the next sub-period due to the low volatility

    and steady positive returns with very few sharp down moves. The results confirm this

    expectation. Exhibits 4c and 5c provide the evidence. In this steadily climbing, near ideal market

    for the QQQ and poor market for the collar, the collar exhibits a far lower return. The annualized

    return of the QQQ over the period is 20.4% at relatively moderate volatility of 17.5%. The 2%

    OTM collar only provides a 5.2% return over this period. It does, however, do so at a far lower

    volatility. In this period, the collar provides about of the returns of the QQQ at less than the

    volatility. By most measures, the collar underperforms the QQQ on a risk-adjusted basis in this

    period. It has a slightly higher maximum drawdown, fewer up-months, a lower Stutzer index, a

    negative information ratio and a -0.26% monthly Leland alpha. It is interesting to note that this

    underperformance is not nearly as significant as the QQQs underperformance in the early

    period.

    The results pertaining to the final sub-period are provided in Exhibits 4d and 5d. This is

    the credit crisis period from October 2007 to May 2009. Once again, the collar provides

    significant capital protection. The -19.8% annualized loss of the QQQ is reduced to only -1.4%,

    while the standard deviation is cut from 29.2% to 11.6%. Therefore, the collar cuts a significant

    loss to less than 1/10 its size while cutting volatility by almost 2/3. Other results confirm the

    collars outperformance in this period. The monthly Leland beta is 0.2%, the information ratio is

    0.77, while the maximum drawdown is reduced from 49.7% to 17.9%.

  • 8/10/2019 Qqq Collar Study

    28/46

    28

    Exhibit 5a Passive Collars with 2% OTM CallsApril 1999 to May 2009

    Mo nthly Data: April, 1999-

    May, 2009

    QQQQ TR

    FUND ONLY -

    No Options

    QQQQ TR PASSIVE

    COLLAR - 2% OTM, 1

    Mo Cal l .0% OTM. 6

    Mo Put .

    QQQQ TR PASSIVE

    COLLAR - 2% OTM, 1M o

    Call.1% OTM. 6 Mo P ut.

    QQQQ TR PA SSIVE

    COLLAR - 2% OTM, 1M o

    Cal l .2% OTM. 6 M o Put .

    QQQQ TR PASSIVE

    COLLAR - 2% OTM, 1M o

    Cal l .3% OTM. 6 Mo Put .

    QQQQ TR PASSIVE

    COLLAR - 2% OTM, 1M o

    Cal l .4% OTM. 6 Mo Put .

    QQQQ TR PASSIVE

    COLLAR - 2% OTM, 1M o

    Cal l .5% OTM. 6 Mo Put .

    Annualized Return -3.57% 8.91% 9.35% 9.26% 9.74% 9.85% 9.89%

    Annualized Std Dev 30.40% 10.27% 10.87% 10.98% 11.10% 11.26% 11.35%

    Sharpe Ratio -0.22 0.57 0.58 0.56 0.60 0.60 0.60

    Annual Stutzer Index -0.07 0.60 0.60 0.59 0.63 0.63 0.62

    C A P M B e t a 1.00 0.09 0.13 0.13 0.15 0.15 0.16

    Leland Beta 1.00 0.08 0.12 0.13 0.14 0.15 0.16

    Mo nthly Leland Alpha 0.00% 0.52% 0.56% 0.56% 0.60% 0.61% 0.62%

    Information Ratio 0.00 0.42 0.46 0.45 0.48 0.48 0.49

    Skew -0.21 0.47 0.20 0.16 0.14 0.06 0.05

    Kurtosis 0.55 4.20 3.68 3.52 3.35 3.24 3.12

    Ma ximum Drawdown -81.08% -18.83% -17.91% -17.90% -17.90% -18.81% -18.81%

    Correlation with QQQ 1.00 0.26 0.36 0.37 0.40 0.42 0.44

    Min M onthly Return -26.20% -7.70% -9.90% -9.95% -9.95% -10.30% -10.30%

    Ma x Monthly Return 23.48% 15.02% 15.06% 15.06% 15.11% 15.11% 15.15%

    Number of Months 122 122 122 122 122 122 122

    % Up Months 52% 63% 63% 65% 64% 63% 61%

    % Down Months 48% 37% 37% 35% 36% 37% 39%

    Exhibit 5b Passive Collars with 2% OTM CallsApril 1999 to September 2002

    Monthly Data: A pr. 1999-Sept,

    2002

    QQQQ TR

    FUND ONLY -

    No Options

    QQQQ TR PA SSIVE

    COLLAR - 2% OTM, 1

    Mo Cal l .0% OTM. 6Mo Put .

    QQQQ TR PASSIVE

    COLLAR - 2% OTM, 1M o

    Call.1% OTM . 6 Mo Put.

    QQQQ TR PA SSIVE

    COLLAR - 2% OTM, 1M o

    Call.2% OTM . 6 Mo Put.

    QQQQ TR PASSIVE

    COLLAR - 2% OTM, 1M o

    Call.3% OTM . 6 Mo Put.

    QQQQ TR PASSIVE

    COLLAR - 2% OTM, 1M o

    Call.4% OTM . 6 Mo Put.

    QQQQ TR PASSIVE

    COLLAR - 2% OTM, 1M o

    Call.5% OTM . 6 Mo Put.

    Annualized Return -23.31% 22.67% 21.48% 21.16% 21.38% 21.43% 20.84%

    Annualized Std D ev 42.44% 13.27% 13.58% 13.69% 13.75% 13.72% 13.86%

    Sharpe Ratio -0.65 1.40 1.28 1.24 1.25 1.26 1.21

    Annual Stutzer Index -0.51 1.34 1.24 1.21 1.22 1.23 1.18

    C A P M B e t a 1.00 0.05 0.08 0.08 0.09 0.09 0.10

    Leland Beta 1.00 0.05 0.08 0.08 0.09 0.10 0.10

    Mo nthly Leland Alpha 0.00% 1.55% 1.51% 1.50% 1.53% 1.54% 1.51%

    Information Ratio 0.00 1.09 1.09 1.08 1.10 1.10 1.10

    Skew 0.14 0.39 0.40 0.39 0.37 0.36 0.38

    Kurtosis -0.70 2.93 2.60 2.47 2.44 2.51 2.41

    Maximum D rawdown -81.08% -7.47% -7.54% -7.54% -7.48% -7.48% -7.48%

    Correlation with QQQ 1.00 0.18 0.25 0.27 0.29 0.30 0.32

    Min M onthly Return -26.20% -7.47% -7.54% -7.54% -7.48% -7.48% -7.48%

    Max M onthly Return 23.48% 15.02% 15.06% 15.06% 15.11% 15.11% 15.15%

    Number of Months 42 42 42 42 42 42 42

    % Up Months 40% 74% 71% 74% 74% 74% 69%

    % Down Months 60% 26% 29% 26% 26% 26% 31%

    Exhibit 5c Passive Collars with 2% OTM CallsOctober 2002 to September 2007

    Mo nthly Data: Sept, 2002 to

    Sept. 2007

    QQQQ TR

    FUND ONLY -

    No Options

    QQQQ TR PA SSIVE

    COLLAR - 2% OTM, 1

    Mo Cal l .0% OTM. 6

    Mo Put .

    QQQQ TR PASSIVE

    COLLAR - 2% OTM, 1M o

    Call.1% OTM . 6 Mo Put.

    QQQQ TR PA SSIVE

    COLLAR - 2% OTM, 1M o

    Call.2% OTM . 6 Mo Put.

    QQQQ TR PASSIVE

    COLLAR - 2% OTM, 1M o

    Call.3% OTM . 6 Mo Put.

    QQQQ TR PASSIVE

    COLLAR - 2% OTM, 1M o

    Call.4% OTM . 6 Mo Put.

    QQQQ TR PASSIVE

    COLLAR - 2% OTM, 1M o

    Call.5% OTM . 6 Mo Put.

    Annualized Return 20.37% 2.91% 5.02% 5.19% 5.79% 6.39% 6.83%

    Annualized Std D ev 17.54% 7.11% 7.91% 7.93% 8.18% 8.32% 8.47%

    Sharpe Ratio 1.00 0.00 0.27 0.29 0.35 0.42 0.46

    Annual Stutzer Index 1.01 0.04 0.30 0.32 0.38 0.44 0.48

    C A P M B e t a 1.00 0.23 0.30 0.30 0.33 0.34 0.36

    Leland Beta 1.00 0.26 0.33 0.33 0.36 0.37 0.38

    Mo nthly Leland Alpha 0.00% -0.35% -0.27% -0.26% -0.26% -0.22% -0.21%

    Information Ratio 0.00 -1.19 -1.13 -1.12 -1.11 -1.08 -1.06

    Skew 0.33 -0.24 -0.21 -0.22 -0.16 -0.18 -0.24

    Kurtosis 1.63 0.14 0.06 0.04 0.16 0.02 -0.08

    Maximum D rawdown -12.36% -16.37% -14.02% -14.02% -13.04% -11.74% -11.74%

    Correlation with QQQ 1.00 0.57 0.67 0.67 0.71 0.71 0.73

    Min M onthly Return -12.09% -5.23% -5.49% -5.49% -5.56% -5.56% -5.56%

    Max M onthly Return 18.47% 4.75% 5.59% 5.59% 6.24% 6.24% 6.24%

    Number of Months 60 60 60 60 60 60 60

    % Up Months 62% 58% 57% 57% 55% 55% 55%

    % Down Months 38% 42% 43% 43% 45% 45% 45%

  • 8/10/2019 Qqq Collar Study

    29/46

    29

    Exhibit 5d Passive Collars with 2% OTM CallsOctober 2007 to May 2009

    Mo nthly Data: Sept, 2007 to

    May. 2009

    QQQQ TR

    FUND ONLY -

    No Options

    QQQQ TR PA SSIVE

    COLLAR - 2% OTM, 1

    Mo Cal l .0% OTM. 6

    Mo Put .

    QQQQ TR PASSIVE

    COLLAR - 2% OTM, 1M o

    Call.1% OTM . 6 Mo Put.

    QQQQ TR PA SSIVE

    COLLAR - 2% OTM, 1M o

    Call.2% OTM . 6 Mo Put.

    QQQQ TR PASSIVE

    COLLAR - 2% OTM, 1M o

    Call.3% OTM . 6 Mo Put.

    QQQQ TR PASSIVE

    COLLAR - 2% OTM, 1M o

    Call.4% OTM . 6 Mo Put.

    QQQQ TR PASSIVE

    COLLAR - 2% OTM, 1M o

    Call.5% OTM . 6 Mo Put.

    Annualized Return -19.78% 0.54% -1.03% -1.44% -0.84% -2.02% -2.02%

    Annualized Std D ev 29.23% 9.54% 11.16% 11.56% 11.64% 12.32% 12.32%

    Sharpe Ratio -0.73 -0.09 -0.22 -0.25 -0.19 -0.28 -0.28

    Annual Stutzer Index -0.67 -0.05 -0.17 -0.20 -0.14 -0.23 -0.23C A P M B e t a 1.00 0.17 0.23 0.25 0.26 0.29 0.29

    Leland Beta 1.00 0.17 0.22 0.24 0.25 0.28 0.28

    Mo nthly Leland Alpha 0.00% 0.23% 0.20% 0.20% 0.26% 0.22% 0.22%

    Information Ratio 0.00 0.79 0.77 0.77 0.81 0.78 0.78

    Skew -0.16 -1.41 -1.72 -1.64 -1.64 -1.55 -1.55

    Kurtosis -0.88 2.32 3.70 3.08 3.04 2.47 2.47

    Maximum D rawdown -49.74% -15.49% -17.91% -17.90% -17.90% -18.81% -18.81%

    Correlation with QQQ 1.00 0.52 0.60 0.62 0.64 0.68 0.68

    Min M onthly Return -15.57% -7.70% -9.90% -9.95% -9.95% -10.30% -10.30%

    Max M onthly Return 13.06% 3.75% 3.84% 3.84% 3.84% 3.95% 3.95%

    Number of Months 20 20 20 20 20 20 20

    % Up Months 50% 55% 65% 70% 70% 65% 65%

    % Down Months 50% 45% 35% 30% 30% 35% 35%

    Active Collars: The next set of exhibits provides results relating to active implementations of the

    collar strategies. Exhibits 6a, 6b, 6c and 6d provide summary statistics for the short, medium and

    long horizon active collar strategies for each of the periods discussed earlier as well as providing

    corresponding statistics for the 2% OTM passive collar and the QQQ.

    Exhibit 6a Active Collar Strategies April 1999 to May 2009

    Mo nthly Data: April, 1999-

    May, 2009

    QQQQ TR

    FUND ONLY -

    No Opt ions

    QQQQ TR PASSIVE

    COLLAR - 2% OTM, 1

    Mo Call .2% OTM. 6

    M o Pu t .

    QQQQ TR Short ACTIVE

    COLLAR - 1M o Call .6 Mo

    Put .

    QQQQ TR M edium ACTIVE

    COLLAR - 1Mo Call .6 Mo

    Put .

    QQQQ TR Long ACTIVE

    COLLAR - 1Mo Call .6 Mo

    Put .

    Annualized Return -3.57% 9.26% 11.55% 10.94% 10.67%

    Annualized Std Dev 30.40% 10.98% 11.44% 11.54% 11.34%

    Sharpe Ratio -0.22 0.56 0.74 0.68 0.67

    Annual Stutzer Index -0.07 0.59 0.75 0.70 0.69

    C A PM B et a 1.00 0.13 0.15 0.15 0.16

    Leland Beta 1.00 0.13 0.14 0.15 0.15

    Mo nthly Leland Alpha 0.00% 0.56% 0.74% 0.70% 0.67%

    Information Ratio 0.00 0.45 0.54 0.52 0.52

    Skew -0.21 0.16 0.01 0.07 -0.07

    Kurtosis 0.55 3.52 3.28 3.26 2.80

    Ma ximum Drawdown -81.08% -17.90% -21.73% -23.57% -23.91%

    Correlation with QQQ 1.00 0.37 0.39 0.41 0.42

    Min M onthly Return -26.20% -9.95% -10.38% -10.38% -10.38%

    Max M onthly Return 23.48% 15.06% 15.41% 15.41% 14.57%

    Number of Mo nths 122 122 122 122 122% Up Months 52% 65% 66% 64% 66%

    % Down Months 48% 35% 34% 36% 34%

  • 8/10/2019 Qqq Collar Study

    30/46

    30

    Exhibit 6a provides statistics covering the overall period. As we mentioned earlier, the

    passive collar clearly outperformed the QQQ in the overall period. The active collar adjustment

    strategy outperformed both the QQQ and the passive collar. All three active collars performed

    similarly, with the short active collar performing the best. While the volatility is slightly higher

    for the short active collar than the passive collar, returns are more than 2% higher annually. This

    is also reflected in the Stutzer index, at 0.75 versus 0.59 for the passive collar. Similarly, the

    monthly Leland alphas are 0.74% and 0.56%, respectively. Therefore, the short active

    implementation of the collar increases the Stutzer index and the Leland alpha both by a factor of

    about . The information ratio is also increased, suggesting that an active implementation does

    provide a benefit to collar performance. On the other hand, maximum drawdown and minimum

    monthly return are both slightly increased in magnitude.

    In the bubble sub-period, the short active collar significantly outperforms the passive

    collar. The active collar generates almost a 1/3 higher annualized return at essentially the same

    standard deviation. Similarly, Exhibit 6b provides evidence that the Stutzer index, Leland alpha

    and information ratio are all significantly higher for the active collar. In fact, in this period, the

    active collar generates almost 2%per monthof Lelands alpha.

  • 8/10/2019 Qqq Collar Study

    31/46

    31

    Exhibit 6b Active Collar Strategies April 1999 to Sept 2002

    Mo nthly Data: Apr. 1999-Sept,

    2002

    QQQQ TR

    FUND ONLY -

    No Options

    QQQQ TR PASSIVE

    COLLAR - 2% OTM, 1

    Mo Call .2% OTM. 6

    Mo Put .

    QQQQ TR Short ACTIVE

    COLLAR - 1Mo Call .6 Mo

    Put .

    QQQQ TR M edium ACTIVE

    COLLAR - 1Mo Call .6 Mo

    Put.

    QQQQ TR Long ACTIVE

    COLLAR - 1Mo Call .6 Mo

    Put .

    Annualized Return -23.31% 21.16% 27.02% 24.27% 25.90%

    Annualized Std Dev 42.44% 13.69% 13.71% 14.13% 13.25%

    Sharpe Ratio -0.65 1.24 1.67 1.43 1.64

    Annual Stutzer Index -0.51 1.21 1.54 1.35 1.52

    C A PM B et a 1.00 0.08 0.11 0.12 0.11

    Leland Beta 1.00 0.08 0.11 0.12 0.11

    Mo nthly Leland Alpha 0.00% 1.50% 1.94% 1.78% 1.87%

    Information Ratio 0.00 1.08 1.26 1.20 1.24

    Skew 0.14 0.39 0.13 0.23 0.12

    Kurtosis -0.70 2.47 2.82 2.55 2.57

    Maximum Drawdown -81.08% -7.54% -7.48% -8.70% -7.54%

    Correlation with QQQ 1.00 0.27 0.33 0.36 0.37

    Min M onthly Return -26.20% -7.54% -7.48% -8.39% -7.54%

    Max M onthly Return 23.48% 15.06% 15.41% 15.41% 14.57%

    Number of Months 42 42 42 42 42

    % Up Months 40% 74% 74% 74% 76%

    % Down Months 60% 26% 26% 26% 24%

    Exhibit 6c provides statistics for the second, unfavorable to the collar, sub-period. In this

    sub-period, the short active strategy significantly mitigates the underperformance of the passive

    strategy. While it still underperforms the QQQ, the monthly Leland beta is improved from a -26

    basis point loss to an -8 basis point loss per month. Similarly, annualized returns are improved

    from 5.2% to 6.7%, while volatility is slightly reduced. The active implementation also improves

    maximum drawdown and minimum monthly return. The improvements of the medium horizon

    active strategy are even more significant in this period.

    The credit crisis sub-period is the only period in which the active strategy underperforms

    the passive strategy (albeit only slightly) and it still significantly outperforms the QQQ. These

    results suggest that a dynamic collar adjustment approach that is actively managed may have

    been able to overcome the small performance deficit between our passive and active strategies.

    However, mayis the operative word. These results are only for the reported time frame and

    might not represent results for future time frames. In addition, there may be alternative

    approaches which provide superior results. Exhibit 6d provides the Leland alpha, which is

    reduced from 20 basis points per month to 13 basis points. Annualized losses are increased from

  • 8/10/2019 Qqq Collar Study

    32/46

    32

    -1.4% to -3.0% and standard deviations are increased slightly from 11.6% to 13.7%. Similarly,

    the information ratio drops from 0.77 to 0.70.

    Exhibit 6c Active Collar Strategies October 2002 to Sept 2007

    Mo nthly Data: Sept, 2002 to

    Sept. 2007

    QQQQ TR

    FUND ONLY -

    No Opt ions

    QQQQ TR PASSIVE

    COLLAR - 2% OTM, 1

    Mo Call .2% OTM. 6

    M o Pu t .

    QQQQ TR Short ACTIVE

    COLLAR - 1M o Call .6 Mo

    Put .

    QQQQ TR M edium ACTIVE

    COLLAR - 1Mo Call .6 Mo

    Put .

    QQQQ TR Long ACTIVE

    COLLAR - 1Mo Call .6 Mo

    Put .

    Annualized Return 20.37% 5.19% 6.72% 7.91% 6.59%

    Annualized Std Dev 17.54% 7.93% 7.68% 7.87% 7.99%

    Sharpe Ratio 1.00 0.29 0.50 0.64 0.46

    Annual Stutzer Index 1.01 0.32 0.52 0.64 0.48

    C A PM B et a 1.00 0.30 0.26 0.28 0.31

    Leland Beta 1.00 0.33 0.29 0.30 0.35

    Mo nthly Leland Alpha 0.00% -0.26% -0.08% -0.01% -0.18%

    Information Ratio 0.00 -1.12 -0.95 -0.88 -1.03

    Skew 0.33 -0.22 -0.08 -0.22 -0.23

    Kurtosis 1.63 0.04 0.80 0.41 0.30

    Ma ximum Drawdown -12.36% -14.02% -9.39% -10.79% -11.85%

    Correlation with QQQ 1.00 0.67 0.59 0.62 0.68

    Min M onthly Return -12.09% -5.49% -5.42% -5.39% -5.39%

    Max M onthly Return 18.47% 5.59% 6.18% 6.18% 6.18%

    Number of Mo nths 60 60 60 60 60

    % Up Months 62% 57% 63% 60% 62%

    % Down Months 38% 43% 37% 40% 38%

    Exhibit 6d Active Collar Strategies October 2007 to May 2009

    Mo nthly Data: Sept, 2007 to

    May. 2009

    QQQQ TR

    FUND ONLY -

    No Opt ions

    QQQQ TR PASSIVE

    COLLAR - 2% OTM, 1

    Mo Call .2% OTM. 6

    M o Pu t .

    QQQQ TR Short ACTIVE

    COLLAR - 1M o Call .6 Mo

    Put .

    QQQQ TR M edium ACTIVE

    COLLAR - 1Mo Call .6 Mo

    Put .

    QQQQ TR Long ACTIVE

    COLLAR - 1Mo Call .6 Mo

    Put .

    Annualized Return -19.78% -1.44% -3.01% -5.02% -5.51%

    Annualized Std Dev 29.23% 11.56% 13.72% 13.27% 13.56%

    Sharpe Ratio -0.73 -0.25 -0.32 -0.49 -0.51

    Annual Stutzer Index -0.67 -0.20 -0.27 -0.45 -0.47

    C A PM B et a 1.00 0.25 0.28 0.24 0.26

    Leland Beta 1.00 0.24 0.27 0.23 0.25

    Mo nthly Leland Alpha 0.00% 0.20% 0.13% -0.10% -0.12%

    Information Ratio 0.00 0.77 0.70 0.60 0.58

    Skew -0.16 -1.64 -0.98 -0.89 -0.91

    Kurtosis -0.88 3.08 0.98 1.26 0.95

    Ma ximum Drawdown -49.74% -17.90% -21.73% -23.57% -23.91%

    Correlation with QQQ 1.00 0.62 0.59 0.54 0.56

    Min M onthly Return -15.57% -9.95% -10.38% -10.38% -10.38%

    Max M onthly Return 13.06% 3.84% 5.64% 5.64% 5.64%

    Number of Mo nths 20 20 20 20 20

    % Up Months 50% 70% 60% 55% 60%

    % Down Months 50% 30% 40% 45% 40%

    Exhibit 7 summarizes many of these results graphically. The exhibit provides an

    illustration of the growth of a $100 investment in the active QQQ collar and the 2% OTM

    passive QQQ collar against the growth of a QQQ investment over the entire period. The

  • 8/10/2019 Qqq Collar Study

    33/46

    33

    difference in the performance of the QQQ and the collar strategies is clearly evident as is the

    added performance gained by implementing the active collar rather than the passive collar.

    Exhibit 7: Growth of $100 in Active and Passive Collar Strategies

    $0.00

    $50.00

    $100.00

    $150.00

    $200.00

    $250.00

    $300.00

    $350.00

    $400.00

    3/19/1999

    9/19/1999

    3/19/2000

    9/19/2000

    3/19/2001

    9/19/2001

    3/19/2002

    9/19/2002

    3/19/2003

    9/19/2003

    3/19/2004

    9/19/2004

    3/19/2005

    9/19/2005

    3/19/2006

    9/19/2006

    3/19/2007

    9/19/2007

    3/19/2008

    9/19/2008

    3/19/2009

    QQQ ShortActive Collar

    QQQ 2% OTMPassive Collar

    QQQ TR

    Exhibit 8: Rolling 12-Month Annualized Returns Active and Passive Collars

    -80.00%

    -60.00%

    -40.00%

    -20.00%

    0.00%

    20.00%

    40.00%

    60.00%

    80.00%

    100.00%

    120.00%

    2/1

    /2000

    8/1

    /2000

    2/1

    /2001

    8/1

    /2001

    2/1

    /2002

    8/1

    /2002

    2/1

    /2003

    8/1

    /2003

    2/1

    /2004

    8/1

    /2004

    2/1

    /2005

    8/1

    /2005

    2/1

    /2006

    8/1

    /2006

    2/1

    /2007

    8/1

    /2007

    2/1

    /2008

    8/1

    /2008

    2/1

    /2009

    Return

    Rolling Annualized Returns

    QQQ Short ActiveCollar

    QQQ Passive 2%OTM Collar

    QQQ TR

    Exhibits 8 and 9 provide rolling 12-month annualized returns and standard deviations,

    respectively. In Exhibit 8 it is clear that the returns to the collar strategies are much more stable

  • 8/10/2019 Qqq Collar Study

    34/46

    34

    than those of the QQQ. In addition, the collars clearly avoid the worst of the negative returns

    near the beginning and at the end of the period.

    The rolling standard deviations provided in Exhibit 9 are evidence of the potential risk

    reduction benefits of the collar strategy. The collar strategies exhibit lower standard deviations

    throughout the entire period, with the difference ranging from about 5% to about 45%. It is also

    worth noting that both exhibits indicate that the benefits of the active collar strategy over the

    passive collar tend to be relatively subtle, particularly when compared to the difference between

    the collars and the QQQ.

    Exhibit 9: Rolling 12-Month Annualized Standard Deviation Active and Passive Collars

    0.0%

    10.0%

    20.0%

    30.0%

    40.0%

    50.0%

    60.0%

    2/1/2000

    8/1/2000

    2/1/2001

    8/1/2001

    2/1/2002

    8/1/2002

    2/1/2003

    8/1/2003

    2/1/2004

    8/1/2004

    2/1/2005

    8/1/2005

    2/1/2006

    8/1/2006

    2/1/2007

    8/1/2007

    2/1/2008

    8/1/2008

    2/1/2009

    StandardDev

    iation

    Rolling Standard Deviation

    QQQ TR

    QQQ ShortActive Collar

    QQQ Passive2% OTM Collar

    Collaring a Mutual Fund

    We also consider applying a collar strategy to a well known small cap equity mutual

    fund. For the analysis, we chose a fund which used the QQQ as a potential passive benchmark

  • 8/10/2019 Qqq Collar Study

    35/46

    35

    and is assumed to track reasonably well with the QQQ. The fund we utilize is from a well-known

    platform, is found in the Morningstar Category Small Growth, and carries a 10-year risk rating

    of Above Average and return rating of Average relative to its peers. Our intention is to

    simulate the practice of applying a collar strategy to a standard equity portfolio on which there

    are no available options written. In such a case, the investor would choose options based on

    liquidity considerations and how well the underlying tracks the investors portfolio.

    Exhibits 10a, 10b, 10c and 10d provide summary statistics for the mutual fund with and

    without the passive and active collar strategies. Before discussing the results, it should be noted

    that the strategies represented are not true collar overlays. The methodology does assume daily

    rebalancing of the option and mutual fund positions to maintain the proper exposure and is thus

    simply a first approximation at the performance of a true collar overlay. In the case of a true

    overlay, far less rebalancing would be required to maintain the collar overlay. In order to easily

    apply these strategies as overlays, the investor could allocate a portion of their portfolio to cash,

    and use this cash reserve to manage the cash flows resulting from the option positions.

    While the active mutual fund collar underperforms the active QQQ collar in the overall

    period (see Exhibit 10a), the improvement on the mutual fund is very significant. The return of

    the active mutual fund collar is more than 4 times the return of the mutual fund, while the

    standard deviation is about 1/3 lower. The Stutzer index increases from 0.12 to 0.45, the

    information ratio (relative to the QQQ) is increased from 0.42 to 0.53, and the monthly Leland

    alpha increases from 0.42% to 0.72%. In addition, maximum drawdown is significantly

    improved from -69.7% to -24.8%. Similar results are found with the passive mutual fund collar.

    The passive mutual fund collar provides a return almost 3 times the return of the mutual fund at

  • 8/10/2019 Qqq Collar Study

    36/46

    36

    about 2/3 the standard deviation, significantly outperforming the mutual fund while slightly

    underperforming the active mutual fund collar.

    In the first (tech bubble) sub-period, the collar strategy significantly improves the returns

    of the mutual fund while reducing the standard deviation. As indicated in Exhibit 10b, the mutual

    fund exhibits a -7.1% annualized loss at a 42.1% standard deviation. In contrast, the passive and

    active mutual fund collars deliver 17.0% and 20.3% returns at 27.2% and 27.6% standard

    deviations, respectively. Similarly, the Stutzer index and Leland alpha are improved from -0.07

    and 1.34% to 0.47 and 1.97% for the passive collar and further improved to 0.58 and 2.24% for

    the active collar.

    Exhibit 10a Mutual Fund Collar Strategies April 1999 to May 2009

    Mo nthly Data: April, 1999-

    May, 2009

    QQQQ TR

    FUND ONLY -

    No Options

    Small Cap Mutual

    Fund FUND ONLY -

    No Options

    Small Cap Mutual Fund

    PASSIVE COLLAR - 2%

    OTM, 1M o Call.2% OTM . 6

    Mo P ut .

    Small Cap Mutual Fund

    Short ACTIVE COLLAR - 1

    Mo C a l l.6 Mo P ut .

    QQQQ TR Short ACTIVE

    COLLAR - 1Mo Call.6 Mo

    Put.

    Annualized Return -3.57% 2.35% 8.37% 9.83% 11.55%

    Annualized Std Dev 30.40% 28.89% 17.90% 18.28% 11.44%

    Sharpe Ratio -0.22 -0.02 0.30 0.37 0.74

    Annual Stutzer Index -0.07 0.12 0.38 0.45 0.75

    C A PM B e ta 1.00 0.84 0.33 0.34 0.15

    Leland Beta 1.00 0.84 0.33 0.33 0.14

    Mo nthly Leland Alpha 0.00% 0.42% 0.60% 0.72% 0.74%

    Information Ratio 0.00 0.42 0.48 0.53 0.54

    Skew -0.21 0.18 1.13 1.07 0.01

    Kurtosis 0.55 1.34 4.98 4.49 3.28

    Maximum Drawdown -81.08% -69.70% -25.27% -24.82% -21.73%

    Correlation with QQQ 1.00 0.89 0.57 0.57 0.39

    Min M onthly Return -26.20% -21.66% -12.01% -12.51% -10.38%

    Max Mo nthly Return 23.48% 27.66% 25.93% 26.03% 15.41%

    Number of Months 122 122 122 122 122

    % Up Mo nths 52% 57% 55% 58% 66%

    % Down Months 48% 43% 45% 42% 34%

  • 8/10/2019 Qqq Collar Study

    37/46

    37

    Exhibit 10b Mutual Fund Collar Strategies April 1999 to September 2002

    Mo nthly Data: Apr. 1999-Sept,

    2002

    QQQQ TR

    FUND ONLY -

    No Opt ions

    Small Cap Mutual

    Fund FUND ONLY -

    No Opt ions

    Small Cap Mutual Fund

    PASSIVE COLLAR - 2%

    OTM , 1M o Call .2% OTM . 6

    M o P u t .

    Small Cap M utual Fund

    Short ACTIVE C OLLAR - 1

    Mo C all .6 Mo P ut .

    QQQQ TR Short ACTIVE

    COLLAR - 1Mo Call .6 Mo

    Put .

    Annualized Return -23.31% -7.05% 16.96% 20.28% 27.02%

    Annualized Std Dev 42.44% 42.14% 27.24% 27.61% 13.71%

    Sharpe Ratio -0.65 -0.27 0.47 0.58 1.67

    Annual Stutzer Index -0.51 -0.07 0.58 0.68 1.54

    C A PM B et a 1.00 0.89 0.40 0.41 0.11

    Leland Beta 1.00 0.89 0.40 0.41 0.11

    Mo nthly Leland Alpha 0.00% 1.34% 1.97% 2.24% 1.94%

    Information Ratio 0.00 0.84 1.21 1.32 1.26

    Skew 0.14 0.41 0.71 0.64 0.13

    Kurtosis -0.70 -0.41 1.12 0.91 2.82

    Ma ximum Drawdown -81.08% -69.70% -25.27% -24.82% -7.48%

    Correlation with QQQ 1.00 0.89 0.62 0.63 0.33

    Min M onthly Return -26.20% -21.66% -12.01% -12.51% -7.48%

    Max M onthly Return 23.48% 27.66% 25.93% 26.03% 15.41%

    Number of Mo nths 42 42 42 42 42

    % Up Months 40% 48% 60% 62% 74%

    % Down Mont


Recommended